Formation Control Algorithm of Agents Based on Earth Mover’s Distance

Abstract

Massive sport, such as unmanned aerial vehicle performance, often needs fast and efficient calculation of formation morphing and individual path planning. This paper introduces a novel fast formation control method of a crowd. First, we get the agents’ location in a 2D polygon with centroidal Voronoi tessellation and L-BFGS techniques. Then, we transform crowd formation shapes with a global shortest motion path pair assignment using earth mover’s distance algorithm. Finally, the repulsing force between agents and obstacles is calculated based on the recursive velocity observer method control agents’ motion. Extensive experimental results show the effectiveness and usefulness of our algorithm in 2D group formation transformation.

Anchor‐based crowd formation transformation

“…The EMD 41 is a vector value proposed to measure the distance between two distributions. In current crowd formation transformation methods, the global shortest moving distance is the most used metric for evaluating formation transformation 18 . Thinking of the crowd formation as the distribution of particles in two‐dimensional (or three‐dimensional) Euclidean space, we can obtain the global shortest total moving distance between the two formations by calculating the EMD.…”

“…In current crowd formation transformation methods, the global shortest moving distance is the most used metric for evaluating formation transformation. 18 Thinking of the crowd formation as the distribution of particles in two-dimensional (or three-dimensional) Euclidean space, we can obtain the global shortest total moving distance between the two formations by calculating the EMD. Determining the EMD is equivalent to building a complete bipartite graph with the negative value of the Euclidean space distance between F i and F i+1 as the edge weight and performing maximum weight matching through the Kuhn-Munkres algorithm.…”

“…This experiment focuses on the impact of different macro-planning results on the crowd formation transformation process. We choose the macro-planning algorithm part of the three typical works 1,3,18 to conduct comparative experiments with the method in this article. In the experiments, we construct two specific crowd formation transformation scenarios to reflect the unique advantages of the proposed method.…”

“…However, low neighborhood continuity does not imply a failure of group formation transformation. This section discusses a simple case 1,18 implemented in many papers to reflect the effect of the formation transformation of different neighborhood continuity crowds. In this experiment, as shown in Figure 9, 1125 agents were constructed to transform a circle (left) into a star (right) by five different methods.…”

“…Li et al 3 successfully applied crowd formation transformation to a crowd performance rehearsal with thousands of people, and realized crowd motion planning based on video input through a multi‐layer model. Liu et al 18 proposed a group formation control algorithm based on the Earth mover's distance (EMD) to achieve group formation movement through global shortest movement path planning. A spectrum‐based approach 19 was also proposed to control the group formation.…”